Preheat the oven to 190 °C / 375 °F. Put the eggs together with sugar in a glass bowl over a saucepan of simmering water. Using an electric mixer, whisk mixture over the heat for about 5 minutes, or until thick, pale and doubled in volume. In a separate bowl combine baking soda, flour and pinch of salt. Sift half of dry mixure into the egg mixute and very gentle fold it through. Sift over the rest of the dry mixture. Again, fold it in gently. Add melted (but cold) butter to the mixture. Grease cake molds with butter, then dust with flour. Divide the mixture between both cake molds. Bake for 20 minutes at 190 °C / 375 °F, until golden and springy to touch. Remove from the oven and let cool completely on a wire rack if possible.
Wash the nectarines under running water and drain them well. Cut them in half and remove the kernels, then cut each half on three pieces. Reserve one nectarine for decoration. Set a saucepan over medium high heat. Add the sugar, slices of ginger and water. Let it slowly simmer for about 5 - 10 minutes or until the sugar caramelizes and gets golden brown. Add pieces of nectarines, rum and leave for about 5 minutes, stirring occasionally. Nectarines have to remain thick. Drain the nectarines and save until needed. Also save the juice.
In a bowl mix together whipping cream and sugar, to get a soft peak. Add 1/3 of the yogurt to the whipping cream mixture and combine well, using a spatula. Gently fold the rest of the yogurt, so that you get a light and airy texture. Refrigerate until needed.
assemble the cake
To assemble the cake, brush both sponge cakes with leftover nectarine juice on one side. Place one sponge cake on a cake stand or serving plate. Arrange pieces of nectarine all over the brushed sponge cake. Dollop on spoonfuls of yogurt cream, leaving 2 tbsp for the decoration later. Cover with the second sponge cake. Decorate with the remaining yogurt cream, arrange the remaining fresh nectarine pieces and dust with icing sugar to finish. Serve with a spoon of greek yogurt. You can store it in a refrigerator for up to 4 days or serve immediately.